Lenses and Waves

210 CHAPTER 5
principle in optics. Still, Huygens’ waves were hypothetical entities. Unlike
Descartes, Huygens did not intend to prove the laws of optics by means of
his theory of waves. It was the other way around: the verities of optics
proved the probability of the way he imagined waves to propagate. The laws
of optics were the ultimate foundation of Huygens’ theory of light. However,
the ‘law’ of strange refraction did not really fit this scheme as it mixed up
waves and rays and was not an empirical truth. Indirectly, via the successful
derivation of the ellipse construction, Huygens’ principle was founded upon
singular – but important – observations of strange refraction. Rømer’s
objections made it clear that the ellipse construction was not the only law
that was consistent with those observations. In order to counter these
objections, Huygens chose to employ the keystone of hypothetico-deductive
inference: experimental verification.
Although he could have refuted Bartholinus’ law otherwise, Huygens
went to the heart of the matter. He devised an experiment with the suggested
relationship between the crystal and strange refraction in mind. An unnatural
section of the crystal would reveal whether a law of strange refraction should
be related to the shape and structure of the crystal or to its material. He put
the very foundation of his wave theory at stake: waves are defined by their
speed of propagation, which depends solely on the medium traversed. This
could not be verified directly, but only by comparing consequences drawn
from the alternatives. The crux of Huygens’ employment of hypotheticodeductive
inference was that he had the laws predict what would happen. He
derived exact predictions to be put to the test. The drawing accompanying
the experiment can be regarded as the essence of Traité de la Lumière: a wave
with respect to an unnatural section. The mathematical representation of the
mechanistic nature of light is here being experimentally verified.
The Eureka of 6 August 1679 was the ultimate consequence of Huygens’
mathematico-mechanistic thinking. Unexpectedly drawn into the problem of
the nature of light, our dioptrical geometer had set up a search for the
mechanistic causes of the properties of light. He had found waves caused by
collisions of ethereal particles and fitted out with mathematically defined
properties. Huygens’ principle was the plausible cause he needed, a law of
waves. It was a new kind of law, unifying the observable properties of light
rays by reference to unobservable waves. It also was a hypothetical law, as it
was not drawn from experience. The ellipse construction derived from it was
likewise hypothetical, although less explicitly so. It described strangely
refracted rays while presupposing spheroidal waves. When forced to test it,
Huygens chose to put to test this assumption of a medium-dependent
propagation of waves. The experiment was not a necessary step, but it was
the obvious choice. Waves were not just a plausible cause of the properties
of light, ultimately they were their true cause. Things could not reasonably be
otherwise than Huygens imagined. Therefore one could deduce phenomena
from this hypothesis, which experiment should show to be real.